Saturday

September 20, 2014

September 20, 2014

Posted by **Ed** on Saturday, July 14, 2007 at 2:15pm.

Use D'Alembert's Rational Roots Theorem. Any rational roots of the form of p/q (p and q assumed to be relatively prime) must be such that p divides the constant term (in this case 4) and q divides the coefficient of the largest power of x (in this case 1).

So, the candidate roots are ±1, ±2, and ±4. If you try these, you see that

x = -1 and x = 2 are roots. There are no other roots, but there must be three roots when we count by multiplicity. So, one of the two roots we found must have a multiplicity of 2.

It isn't difficult to see that this must be the root x = 2, because then you get the correct factorization:

(x+1)(x-2)^2

**Answer this Question**

**Related Questions**

math - List all possible rational zeros of... h(x)= 2x to the (4th power) - 5x (...

ALGEBRA 2 - Use the Rational Root Theorem to list all possible rational roots ...

algebra - Factor this polynomial: F(x)=x^3-x^2-4x+4 Try to find the rational ...

algebra 2 - Factor completely with respect to the integers. 1. 9x^2 - 4 2. x^3...

Math - Rational Roots - 1.) What are the possible rational roots of the function...

math - I HAVE THESE ANSWERS FOR THE PROBLEMS. COULD YOU DOUBLE CHECK PLEASE, ...

math - Could you please solve so I can double check my answers for the practice ...

College Algebra--Still Confused - I have a few problems I need help with and ...

College Algebra - I have a few problems I need help with and also do have ...

Pre-Calc-Please check - Is this correct? Using Rational Roots Theorem, list all...